An Interlude….

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Presentation transcript:

An Interlude…

Arc Lengths and Surface Areas How can we use a Riemann Sum to find the length of a curve?

Arc Length “s” Example: what is the length along the parabola y = x2 from x = 0 to x = 2?

How about Surface Area? Develop an expression for the surface area of the surface formed by rotating y = 1/x around the x-axis between x = 1 and x = 10 Generalize for all functions f(x), show that:

The strange case of “Gabriel’s Horn” Which is bigger The volume of revolution formed by rotating y = 1/x around the x-axis from x = 1 to infinity? or The surface area formed by rotating y = 1/x around the x-axis from x = 1 to infinity? Now, back to the salt mines!